options nodate nonumber ps=55 ls=80;

title 'RPD -- Example 12.2 -- Poisson Variance Stabilization (Simulation)';

data simpoisson;
do x = 1 to 30 by 0.05;
y = ranpoi(1234,x);   /* Poisson variate with mean x (using 1234 as a seed) */
output;
end;
run;


proc reg;
model y = x;

plot residual.*predicted. / nomodel nostat;
run;


data simpoisson;
set simpoisson;
sqrty = sqrt(y);
sqrtx = sqrt(x);
run;


/* Try variance stabilizing transformation: */

proc reg;
model sqrty = x;

plot residual.*predicted. / nomodel nostat;
run;


/* Attempt to restore straight-line mean relationship: */

proc reg;
model sqrty = sqrtx;

plot residual.*predicted. / nomodel nostat;
run;